hi, its a really old fashioned song and has been used in other movies aswell. It plays at the start of "Out Of The Blue", when your are seeing around the whole town. I think the lyrics go something like "... I promsie to be true and to love only you.. ". it's quite a slow old song.
could be smoke gets in your eyes by the platters - never actually seen the film just going by the lyrics you've posted and the description of the song
hth x